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Register a new userA tractable Bayesian joint model for longitudinal and survival data
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Added by
Francisco Javier Rubio
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modelled using generalised linear mixed models, while the survival process is modelled using a parametric general hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of non-linear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modelling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyse the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.
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Joint modelling of longitudinal and time-to-event data is usually described by a random effect joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the latent effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas, to introduce non-linear correlation between the marginal distributions of the longitudinal and time-to-event processes. A Gaussian copula joint model has been proposed in the literature to fit joint data by applying a Monte Carlo expectation-maximisation algorithm. Enlightening as it is, its original estimation procedure comes with some limitations. In the original approach, the log-likelihood function can not be derived analytically thus requires a Monte Carlo integration, which not only comes with intensive computation but also introduces extra variation/noise into the estimation. The combination with the EM algorithm slows down the computation further and convergence to the maximum likelihood estimators can not be always guaranteed. In addition, the assumption that the length of planned measurements is uniform and balanced across all subjects is not suitable when subjects have varying number of observations. In this paper, we relax this restriction and propose an exact likelihood estimation approach to replace the more computationally expensive Monte Carlo expectation-maximisation algorithm. We also provide a straightforward way to compute dynamic predictions of survival probabilities, showing that our proposed model is comparable in prediction performance to the shared random effects joint model.
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